The rainbow vertex connection number of star wheel graphs

Abstract

A vertex-colored graph G = (V(G), E(G)) is said to be rainbow vertex-connected, if for every two vertices u and v in V(G), there exists a u – v path with all internal vertices have distinct colors. The rainbow vertex connection number of G, denoted by rvc(G), is the smallest number of colors needed to make G rainbow vertex connected. In this paper, we determine the rainbow vertex connection number of star wheel graphs.